{"title":"带终点约束的线性随机控制系统的部分可控性及其在带跳跃的博弈控制系统中的应用","authors":"Yuanzhuo Song","doi":"10.1137/22m1537114","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3635-3663, December 2023. <br/> Abstract. In this paper, we consider the partial controllability of linear stochastic control systems with terminal constraints. Some necessary and sufficient conditions for this controllability are obtained with the help of backward stochastic differential equations (BSDEs). We establish the equivalence between the controllability of a game-based control system (GBCS), the controllability of a forward backward stochastic differential equation (FBSDE), and the partial controllability of a related stochastic differential equation (SDE) with terminal constraints. By applying our results, we obtain some necessary and sufficient conditions for the controllability of GBCSs with jumps. Then we embed the GBCSs driven only by Brownian motion and deterministic GBCSs into our framework with jumps. Previous results of Zhang and Guo are covered and extended.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":"38 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Partial Controllability of Linear Stochastic Control Systems with Terminal Constraints and Its Applications to Game-Based Control Systems with Jumps\",\"authors\":\"Yuanzhuo Song\",\"doi\":\"10.1137/22m1537114\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3635-3663, December 2023. <br/> Abstract. In this paper, we consider the partial controllability of linear stochastic control systems with terminal constraints. Some necessary and sufficient conditions for this controllability are obtained with the help of backward stochastic differential equations (BSDEs). We establish the equivalence between the controllability of a game-based control system (GBCS), the controllability of a forward backward stochastic differential equation (FBSDE), and the partial controllability of a related stochastic differential equation (SDE) with terminal constraints. By applying our results, we obtain some necessary and sufficient conditions for the controllability of GBCSs with jumps. Then we embed the GBCSs driven only by Brownian motion and deterministic GBCSs into our framework with jumps. Previous results of Zhang and Guo are covered and extended.\",\"PeriodicalId\":49531,\"journal\":{\"name\":\"SIAM Journal on Control and Optimization\",\"volume\":\"38 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-12-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Control and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1537114\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Control and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1537114","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
The Partial Controllability of Linear Stochastic Control Systems with Terminal Constraints and Its Applications to Game-Based Control Systems with Jumps
SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3635-3663, December 2023. Abstract. In this paper, we consider the partial controllability of linear stochastic control systems with terminal constraints. Some necessary and sufficient conditions for this controllability are obtained with the help of backward stochastic differential equations (BSDEs). We establish the equivalence between the controllability of a game-based control system (GBCS), the controllability of a forward backward stochastic differential equation (FBSDE), and the partial controllability of a related stochastic differential equation (SDE) with terminal constraints. By applying our results, we obtain some necessary and sufficient conditions for the controllability of GBCSs with jumps. Then we embed the GBCSs driven only by Brownian motion and deterministic GBCSs into our framework with jumps. Previous results of Zhang and Guo are covered and extended.
期刊介绍：
SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition.
The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.
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